We report large nonreciprocal optical absorption at shortwave infrared (SWIR) wavelengths in the magnetoelectric (ME) antiferromagnet (AFM) LiNiPO_{4}. The difference in absorption coefficients for light propagating in opposite directions, divided by the sum, reaches up to ∼40% at 1450 nm. Moreover, the nonreciprocity is switched by a magnetic field in a nonvolatile manner. Using symmetry considerations, we reveal that the large nonreciprocal absorption is attributed to Ni^{2+} d-d transitions through the spin-orbit coupling. Furthermore, we propose that an even larger nonreciprocity can be achieved for a Ni-based ME AFM where electric dipoles of every NiO_{6} unit and Ni^{2+} spins are orthogonal and, respectively, form a collinear arrangement. This study provides a pathway toward nonvolatile switchable one-way transparency of SWIR light.